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Partial Differential Equations II : Qualitative Studies of Linear Equations

by Michael Taylor. -- 1st ed. 1996. -- Springer New York, 1996. -- (Applied Mathematical Sciences ; 116). w. <EB00021421>
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Partial Differential Equations II : Qualitative Studies of Linear Equations

by Michael Taylor. -- 1st ed. 1996. -- Springer New York, 1996. -- (Applied Mathematical Sciences ; 116). w. <EB00021421>
Tag:
No tag is registered
Functions:
Details
URL:

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IDENT https://doi.org/10.1007/978-1-4757-4187-2
title and statement of responsibility area Partial Differential Equations II : Qualitative Studies of Linear Equations / by Michael Taylor
specific material designation code Remote
edition area 1st ed. 1996
publication,distribution,etc.,area New York, NY : Springer New York : Imprint: Springer , 1996
physical description area XXI, 529 p. 11 illus : online resource
Volume Information
ISBN 9781475741872
parent bibliography link Applied Mathematical Sciences <> 116//a
contents of works 7 Pseudodifferential Operators
contents of works 8 Spectral Theory
contents of works 9 Scattering by Obstacles
contents of works 10 Dirac Operators and Index Theory
contents of works 11 Brownian Motion and Potential Theory
contents of works 12 The ??-Neumann Problem
contents of works C Connections and Curvature
note Partial differential equations is a many-faceted subject. Created to describe the mechanical behavior of objects such as vibrating strings and blowing winds, it has developed into a body of material that interacts with many branches of math­ ematics, such as differential geometry, complex analysis, and harmonic analysis, as weil as a ubiquitous factor in the description and elucidation of problems in mathematical physics. This work is intended to provide a course of study of some of the major aspects of PDE. It is addressed to readers with a background in the basic introductory grad­ uate mathematics courses in American universities: elementary real and complex analysis, differential geometry, and measure theory. Chapter 1 provides background material on the theory of ordinary differential equations (ODE). This includes both very basic material-on topics such as the existence and uniqueness of solutions to ODE and explicit solutions to equations with constant coefficients and relations to linear algebra-and more sophisticated results-on flows generated by vector fields, connections with differential geom­ etry, the calculus of differential forms, stationary action principles in mechanics, and their relation to Hamiltonian systems. We discuss equations of relativistic motion as weIl as equations of c1assical Newtonian mechanics. There are also applications to topological results, such as degree theory, the Brouwer fixed-point theorem, and the Jordan-Brouwer separation theorem. In this chapter we also treat scalar first-order PDE, via Hamilton-Jacobi theory
NCID 9780387946511
text language code English
author link *Taylor, Michael <> author
author link SpringerLink (Online service) <>
classification DC23:515
subject headings Mathematical analysis
subject headings Analysis (Mathematics)
subject headings Probabilities
subject headings Mathematical physics
subject headings Analysis
subject headings Probability Theory and Stochastic Processes
subject headings Theoretical, Mathematical and Computational Physics
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